Readout-only excitation of transverse cavity eigenmodes

Abstract

Using numerical simulations, we study when photodetector-only feedback can selectively excite a transverse eigenmode of an optical cavity by optimizing a phase-only input wavefront. The distinction between spectral distinguishability and mode control is crucial: the phase mask can redistribute input power among cavity modes, whereas the detector can distinguish modes only if their detuning-dependent spectral responses differ. A general consequence is that modes with identical detuning weights are not distinguishable from any finite set of photodetector samples. Exact spectral degeneracy therefore makes only the total power in the degenerate group observable. We demonstrate this information limit using Hermite–Gaussian fixed-order families with prescribed pre-existing astigmatic splitting, Lorentzian spectral weights, and a single-plane phase-control model. In this setting, splitting already present in the cavity makes competing modes spectrally distinguishable, whereas the readout strategy only exploits this distinguishability and does not create it. Simulations comparing single- and multi-detuning objectives at equal photodetector-sample count show that additional detuning probes can improve within-order selectivity in the weak-to-moderate splitting regime, whereas single-detuning operation can remain favorable for throughput.